After some thought, I decided to remove the calculator completely for now. My reasoning is that there is a reason why Shopify cart and checkout is set up like this.
Shipping charges are an extra hurdle that can deter some customers, some customers are likely to drop off after finding out the charges.
If you inform a new customer before they begin checkout you will never receive their details to re-engage them after they drop off (aka, you never get their email).
This is probably why Shopify checkout asks customers to fill in their email and details before proceeding to the shipping choice page.
Customers who drop off due to shipping can be re-engaged with an abandoned cart email, you can even then offer free shipping or a discount to try to rewin the sale.
Adding a shipping estimate before checkout breaks the flow designed by Shopify to get details of customers allowing abandoned carts to be won.